The best way to find houses is to give your criteria to a realtor and have them sign you up for MLS listing emails. It's free, although it does involve finding a realtor first. (But that should be your focus anyway.) Sites like Zillow (redfin is better in my opinion) sometimes have outdated or wrong info.

You could also start going to open houses, speaking to realtors there and see who gives you good/knowledgeable vibes.

As for a down payment, there are options that exist outside of the 20% down, like FHA loans or an 80-10-10 loan. Especially with that household income.